Continuum modeling of gas-particle flows across multiple scales
William Holloway
Graduate Research Fellow
Princeton University
Abstract
Reacting gas-particle flows are encountered throughout the chemical process industry, with applications ranging from the synthesis of specialty chemicals to catalytic cracking and coal conversion. Gas-particle flows in these systems exhibit persistent fluctuations in velocity and particle volume fraction that span a wide range of length and time scales. These flow structures arise as a consequence of the instability of the uniformly fluidized state [1], and can be predicted via continuum models that treat the particle and fluid phases as interpenetrating continua [2]. These models commonly take the form of balance equations for particle and fluid phase mass and momentum, with an additional evolution equation governing the fluctuating motion of the particle phase. While the continuum model framework is capable of predicting these flow structures, very fine grid resolutions are required to accurately resolve all relevant length scales (on the order of 10 particle diameters) [3]. Such fine resolution is not affordable when simulating gas-particle flows large devices, and much coarser grid resolutions are generally employed.
Recently, filtered models have been developed for the affordable (and accurate) simulation of non-reacting gas-particle flows on coarse numerical grids. Such simulations capture coarse macro-scale flow structures, but do not explicitly resolve the fine structures in the simulation. Instead the consequences of these fine structures appear in the filtered model through filtered constitutive models [4]. The present study is concerned with the extension of previous work to reacting gas-particle flows. Coarse-grid simulations of reacting multiphase flows require filteredspecies and energy balances, in addition to the filtered hydrodynamic equations that have already been developed. In the present study we construct filtered balance equations for gaseous reactants participating in catalytic reactions on porous particles. Such coarse-grained equations call for filtered chemical reaction rates, which should account for modification of the reaction rates brought about by meso-scale inhomogeneous flow structures.
To this end we have performed highly resolved simulations of gas-particle flow in the presence of a solid catalyzed, irreversible, first order, isothermal reaction. Our simulations reveal that the cluster effectiveness factor associated with meso-scale structures decreases systematically with increasing filter size and reaction rate constant. This implies that coarse-grid simulations of reacting multiphase flows will overestimate conversions if proper allowances are not made for the decreased effectiveness of the catalyst. A model for the cluster-scale effectiveness factor will be presented, which was constructed by filtering high-resolution reacting gas-particle flow simulations.
[1] Sangani A, Koch, DL. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid. Mech. 1999; 400: 229-263.
[2] Jackson R, The Dynamics of Fluidized Particles. Cambridge University Press: Cambridge, 2000.
[3] Agrawal K, Loezos, PN, Syamlal, M, Sundaresan, S. The role of meso-scale structures in rapid gas-solid flows.J. Fluid. Mech. 2001; 445: 151-185
[4] Igci, Y, Andrews, AT, Sundaresan, S, Pannala, S, O’Brien, T. Filtered two-fluid models for fluidized gas-particle suspensions. AIChE J. 2008; 54: 1431-1448